Algebra Examples

$f (x) = \frac{x^{2} - 1}{x^{2} + 3 x + 2}$

Step 1

Set $\frac{x^{2} - 1}{x^{2} + 3 x + 2}$ equal to $0$ .

$\frac{x^{2} - 1}{x^{2} + 3 x + 2} = 0$

Step 2

Solve for $x$ .

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Step 2.1

Set the numerator equal to zero.

$x^{2} - 1 = 0$

Step 2.2

Solve the equation for $x$ .

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Step 2.2.1

Add $1$ to both sides of the equation.

$x^{2} = 1$

Step 2.2.2

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

$x = \pm \sqrt{1}$

Step 2.2.3

Any root of $1$ is $1$ .

$x = \pm 1$

Step 2.2.4

The complete solution is the result of both the positive and negative portions of the solution.

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Step 2.2.4.1

First, use the positive value of the $\pm$ to find the first solution.

$x = 1$

Step 2.2.4.2

Next, use the negative value of the $\pm$ to find the second solution.

$x = - 1$

Step 2.2.4.3

The complete solution is the result of both the positive and negative portions of the solution.

$x = 1, - 1$

Step 2.3

Exclude the solutions that do not make $\frac{x^{2} - 1}{x^{2} + 3 x + 2} = 0$ true.

$x = 1$

Step 3